according to the Scale of 10 in an inch Take in your Compasses the length of the line AB and applying it to your Scale of 10 in an Inch you shall finde the extent of the Compasses to reach from 5 of the great divisions to fix of the lesser divisions wherefore the line AB contains 5 Chains and 60 Links The like must be done for any other line and also by any of the other Scales Upon the Ruler there is besides the severall Scales of equall parts a Line or Scale of Chords which is numbered by 10 20 30 c. to 90 and this line serveth to protract or lay down angles but in all the prectise of Surveying a Protractor is much more convenient yet for other uses this line may be very serviceable and when a Protractor is wanting it may supply that defect the manner how to use it is thus 3. How to lay down upon paper an angle containing any number of degrees and minutes by the Line of Chords Draw a line at pleasure as AB and from the point A let it be required to protract an angle of 40 degrees 20 minutes First extend your Compasses upon the line of Chords from the beginning thereof to 60 degrees alwayes and with this distance setting one foot upon the point A with the other describe the pricked arch BC then with your Compasses take 40 degrees 20 minutes which is the quantity of the inquired angle out of the line of Chords from the beginning thereof to 40 degrees 20 minutes then the Compasses so resting if you set one foot thereof upon B the other will reach upon the arch to C. Lastly draw the line AC so the angle CAB shall contain 40 degrees 20 minutes 4. Any angle being given to finde what number of degrees and minutes are contained therein Suppose CAB were an angle given and that it were required to finde the quantity thereof Open your Compasses as before to 60 degrees of your Chord and placing one foot in 〈◊〉 with the other describe the arch CB then take in your Compasses the distance CB and measuring that extent upon the little of Chords from the beginning thereof you shall finde it to reach to 40 degrees 20 minutes which is the quantity of the required angle If any angle given or required shall contain above 20 degrees you must then protract it at twice by taking first the whole line and then the remainder CHAP. II. Of the use of the Protractor ALthough the chiefe uses of the Protractor may be performed by the line of Chords last spoken of yet for avoyding of superfluous lines and arches which must otherwise be drawn all over your Plot the Protractor is far more convenient the 〈◊〉 â—ereof is 1. To lay down upon paper an angle of any quantity First draw a right line at length as AB then on any part thereof as on C place the center of the Protractor in which point also fix your protracting pin and turn the Protractor about upon the center till the Meridian line of the Protractor noted in the description thereof with EF lie directly on this line AB the Semicircle of the Protractor lying upwards or from you then close to the edge of the Semicircle at the division of 50 degrees mark the point D with your protracting pin and draw the line CD so shall the angle DCA contain 50 degrees 2. Any angle being given to finde the quantity thereof by the Protractor Suppose DCB were an angle given and that it were required to finde the quantity thereof by the Protractor First you must apply the center of the Protractor to the point C and the Meridian line thereof directly upon the line DC then shall you finde the line CB to lie directly under 130 degrees of the Protractor and such is the quantity of the angle DCB required CHAP. III. Of the Plain Table how to set the parts thereof together and make it fit for the field WHen you would make your Table fit for the field lay the three boards thereof togethâ— and also the ledges at each end thereof in their due plaâ—…â—ccording as they are marked Then lay a sheet of white paper 〈◊〉 over the Table which must be stretched over all the boards by putting on the Frame which bindes both the paper to the boards and the boards one to another Then screw the Socket on the back side of the Table and also the Box and Needle in its due place the Metidian line of the Card which is in the Box lying parallel to the Meridian or Diameter of the Table which diameter is a right line drawn upon the Table from the beginning of the degrees through the center and so to the end of the degrees Then put the Socket upon the head of the Staffe and there screw it Also put the sights into the Index and lay the Index on the Table so is your Instrument prepared for use as a Plain Table or Theodolite the difference only being in placing of the Index for when you use your Instrument as a Plain Table you may pitch your center in any part of the Table which you shall think most convenient for the bringing on of the work which you intend But if you use your Instrument as a Theodolite then the Index must be turned about upon the Center of the Table for which purpose there is a piece of wier which goes through a small hole of brasse fastened to the Index and so into the center by which means the Index keepes his constant place only moving upon the center Your Instrument being thus ordered you may use it either as a Plain Table or a Theodolite but if you would use it as a Circumferentor you need only screw the Box and Needle to the Index and both of them to the head of the Staffe with a brasse screw-pin fitted for that purpose so that the Staffe being fixed in any place the Index and fights may turn about at pleasure without moving of the Staffe and now is your Instrument a good Circumferentor nay better then that before described in the second Book Also when you have occasion to measure any Altitude hang the Labell upon the farther Sight and thus are you exactly fitted for all occasions CHAP. IV. How to measure the quantity of any angle in the field by the Plain Table Theodolite and Circumferentor and also to observe an angle of Altitude YOu must understand that when I mention the Plain Table or perform any work thereby that I mean the Table when it is covered with a sheet of paper upon which all observations of angles that are taken upon the Table in the field do agree exactly in proportion with those of the field it selfe but are not denominated by their quantities but by their symetry or proportion Secondly When I mention the Theodolite or work by that Instrument I do not mean the Theodolite before described in the 2 Chapter of the 2 Book but I mean the degrees described
To reduce Acres into Perches and the contrary 248. 19. The use of a Scale of Reduction necessary for finding the Fraction parts of an Acre 250 20. Divers compendious rules for the ready casting up of any plain Superficies with divers other Compendiums in Surveying by the line of Numbers 251. 21. Of Satute and Customary measure to reduce one to the other at pleasure 254. 22. Of the laying out of common fields into furlongs 255. 23. Of Hils and Mountains how to finde the lengths of the horizontall lines on which they stand severall wayes 257 24. Of mountanous and uneven grounds how to protract or lay the same down in plano after the best manner giving the area or content thereof 258. 25. How to take the Plot of a whole Manner by the Plain Table three severall ways 260. Circumferentor 266. or Peractor 266. With the keeping an account in your Field-book after the best and most certain manner 270. and to protract any observations so taken 271. 26. Of inlarging or diminishing of Plots according to any possible proportion by Two Semicircles Mr. Rathborns Ruler A Line into 100 parts The Parallelogram 273. 27 Of conveying of water 276. FOrasmuch as the whole Art of Surveying of Land is performed by Instruments of severall kindes and that the exact and carefull making and dividing of all such Instruments is chiefely to be aimed at I thought good to intimate to such as are desirous to practise this Art and do not readily know where to be furnished with necessary Instruments for the performance thereof that all or any of the Instruments used or mentioned in this Book or any Mathematicall Instrument whatsoever is exactly made by Mr. Anthony Thompson in Hosier lane neer Smithfield London THE COMPLEAT SURVEYOR The First Book THE ARGVMENT THis first Book consisteth of divers Definitions Problemes Geometricall extracted out of the Writings of divers ancient and modern Geometricians as Euclid Ramus Clavius c. and are here so methodically disposed that any man may gradually proceed from Probleme to Probleme without interruption or being referred to any other Author for the Practicall performance of any of them Onely the Demonstration is wholly omitted partly because those Books out of which they were extracted are very large in that particular and also for the avoiding of many other Propositions and Theoremes which had the ensuing Problemes been demonstrated must of necessity have been inserted Also the figures would have been so incumbred with multiplicity of lines that the intended Problemes would have been thereby much darkened And besides it was not my intent in this place to make an absolute or entire Treatise of Geometry and therefore I have onely made choice of such Problems as I conceived most usefull for my present purpose and come most in use in the practice of Surveying and ought of necessity to be known by every man that intendeth to exercise himselfe in the Practice thereof and those are chiefly such as concern the reducing of Plots from one forme to another and to inlarge or diminish them according to any assigned Proportion also divers of the Problemes in this Book will abundantly help the Surveyor in the division and seperation of Land and in the laying out of any assigned quantity whereby large parcels may be readily divided into divers severals and those again sub-divided if need be Also for the better satisfaction of the Reader I have performed divers of the following Problemes both Arithmetically and Geometrically GEOMETRICALL DEFINITIONS 1. A Point is that which cannot be divided A Point or Signe is that which is void of all Magnitude and is the least thing that by minde and understanding can be imagined and conceived than which there can be nothing lesse as the Point or Prick noted with the letter A which is neither quantity nor part of quantity but only the terms or ends of quantity and herein a Point in Geometry differeth from Unity in Number 2. A Line is a length without breadth or thicknesse A Line is created or made by the moving or drawing out of a Point from one place to another so the Line AB is made by moving of a Point from A to B and according as this motion is so is the Line thereby created whether streight or crooked And of the three kindes of Magnitudes in Geometry viz. Length Breadth and Thicknesse a Line is the first consisting of Length only and therefore the Line AB is capable of division in length only and may be divided equally in the point C or unequally in D and the like but will admit of no other dimension 3. The ends or bounds of a Line are Points This is to be understood of a finite Line only as is the line AB the ends or bounds whereof are the points A and B But in a Circular Line it is otherwise for there the Point in its motion returneth again to the place where it first began and so maketh the Line infinite and the ends or bounds thereof undeterminate 4. A Right line is that which lieth equally between his points As the Right line AB lyeth streight and equall between the points A and B which are the bounds thereof without bowing and is the shortest of all other lines that can be drawn between those two points 5. A Superficies is that which hath only length and breadth As the motion of a point produceth a Line the first kinde of Magnitude so the motion of a Line produceth a Superficies which is the second kinde of Magnitude and is capable of two dimensions namely length and breadth and so the Superficies ABCD may be divided in length from A to B and also in breadth from A to C. 6. The extreams of a Superficies are Lines As the extreams or ends of a Line are points so the extreams or bounds of a Superficies are Lines and so the extreams or ends of the Superficies ABCD are the lines AB BD DC and CA which are the terms or limits thereof 7. A plain Superficies is that which lieth equally between his lines So the Superficies ABCD lieth direct and equally between his lines and whatsoever is said of a right line the same is also to be understood of a plain Superficies 8. A plain Angle is the inclination or bowing of two lines the one to the other the one touching the other not being directly joyned together As the two lines AB and BC incline the one to the other and touch one another in the point B in which point by reason of the inclination of the said lines is made the Angle ABC But if the two lines which touch each other be without inclination and be drawn directly one to the other then they make no angle at all as the lines CD and DE touch each other in the point D and yet they make no angle but one continued right line ¶ And here note that an Angle commonly is signed by three Letters the middlemost whereof sheweth
equall 2. If any right line fall upon two parallel right lines it maketh the outward angles on the one equall to the inward angles on the other and the two inward opposite angles on contrary sides of the falling line also equall 3. If any side of a Triangle be produced the outward angle is equall to the two inward opposite angles and all the three angles of any Triangle are equall to two right angles 4. In equiangled Triangles all their sides are proportionall as well such as contain the equall angles as also the subtendent sides 5. If any four Quantities be proportionall the first multiplied in the fourth produceth a Quantity equall to that which is made by multiplication of the second in the third 6. In all right angled Triangles the square of the side subtending the right angle is equall to both the squares of the containing sides 7. All parallelograms are double to the triangles that are described upon their bases their altitudes being equall 8. All triangles that have one and the same Base and lie between two parallel lines are equall one to the other GEOMETRICALL PROBLEMES PROBLEME I. Vpon a right line given how to erect another right line which shall be perpendicular to the right line given THe right line given is AB upon which from the point E it is required to erect the perpendicular EH Opening your Compasses at pleasure to any convenient distance place one foot in the assigned point E and with the other make the marks C and D equidistant on each side the given point E. Then opening your Compasses again to any other convenient distance wider then the former place one foot in C and with the other describe the arch GG also the Compasses remaining at the same distance place one foot in the point D and with the other describe the arch FF then from the point where these two arches intersect or cut each other which is at H draw the right line HE which shall be perpendicular to the given right line AB which was the thing required to be done PROB. II. How to erect a Perpendicular on the end of a right line given LEt OR be a line given and let it be required to erect the perpendicular RS. First upon the line OR with your Compasses opened to any small distance make five small divisions beginning at R noted with 1 2 3 4 5. Then take with your Compasses the distance from R to 4 and placing one foot in R with the other describe the arch PP Then take the distance R 5 and placing one foot of the Compasses in 3 with the other foot describe the arch BB cutting the former arch in the point S. Lastly from the point S draw the line RS which shall be perpendicular to the given line OR PROB. III. How to let fall a perpendicular from any point assigned upon a right line given THE point given is C from which point it is required to draw a right line which shall be perpendicular to the given right line AB First from the given point C to the line AB draw a line by chance as CE which divide into two equall parts in the point D then placing one foot of the Compasses in the point D with the distance DC describe the Semicircle CFE cutting the given line AB in the point F. Lastly if from the point C you draw the right line CF it shall be a perpendicular to the given line AB which was required PROB. IV. How to make an angle equall to an angle given LEt the angle given be ACB and let it be required to make another angle equall thereunto First draw the line EF at pleasure then upon the given angle at C the Compasses opened to any distance describe the ark AB also upon the point F the Compasses un-altered describe the arke DE then take with your Compasses the distance AB and set the same distance from E to D. Lastly draw the line DF so shall the angle DFE be equall to the given angle ACB PROB. V. A right line being given how to draw another right line which shall be parallel to the former at any distance required THe line given is AB unto which it is required to draw another right line parallel thereunto at the distance AC or BD. First Open your Compasses to the distance AC or AD then placing one foot in A with the other describe the arke C also place one foot in B and with the other describe the arch D. Lastly Draw the line CD so that it may only touch the arks C and D so shall the line CD be parallel to the line AB and at the distance required PROB. VI. To divide a right line given into any number of equall parts LEt AB be a line given and let it be required to divide the same into four equall parts First From the end of the given line A draw the line AC making any angle then from the other end of the given line which is at the point B draw the line BD parallel to AC or make the angle ABD equall to the angle CAB then upon the lines AC and BD set off any three equall parts which is one lesse then the number of parts into which the line AB is to be divided on â—ace line as 1 2 3 then draw lines from 1 to 3 from 2 to 2 and from 3 to 1 which lines crossing the given line AB shall divide it into four equall parts as was required PROB. VII A right line being given how to draw another right line parallel thereunto which shall also passe through a point assigned LEt AB be a line given and let it be required to draw another line parallel thereunto which shall passe through the given point C. First Take with your compasses the distance from A to C and placeing one foote thereof in B with the other describe the ark DE then take in your compasses the whole line AB and placing one foot in the point C with the other describe the arke FG crossing the former arke DE in the point H. Lastly if you draw the line CH it shall be parallel to AB PROB. VIII Having any three points given which are not situate in a right line how to finde the center of an arch of a Circle which shall passe directly through the three given points THe three points given are A B and C now it is required to finde the center of a Circle whose circumference shall passe through the three points given First Opening your Compasses to any distance greater then halfe BC place one foot in the point B and with the other describe the arch FG then the Compasses remaining at the same distance place one foot in C and with the other turned about make the marks F and G in the former arch and draw the line FG at length if need be Again opening the Compasses to any distance greater then halfe AB place one foot in
draw the right line GP which shall divide the whole Plot ABCDEF into two parts being in proportion one to the other as the line T is to the line S. PROB. XXXVIII How to divide an irregular Plot according to any proportion by a line drawn from any angle thereof LEt ABCDEFG be an irregular Plot and let it be required to divide the same into two equall parts by a line drawn from the angle A. First draw the line HK dividing the Plot into two parts namely into the five sided figure ABCFG and into the Trapezia FCED then by the 31 Probleme reduce the five sided figure ABCFG into the Triangle HAK the base whereof HK divide into two equall parts in O and draw the line OA which shall divide the five sided figure ABCFG into two equall parts Then by the 30 Probleme reduce the Trapezia FCDE into the Triangle OLM and divide the base thereof LM into two equall parts in the point P and draw the line OP which will divide the Trapezia FCDE into two equall parts and so is the whole Plot divided into two equall parts by the lines AO and OP but to performe the Probleme by one right line only do thus from the point A draw the line AP and parallel thereunto through the point O draw the line ON Lastly if you draw a right line from A to N it shall divide the whole Plot into two equall parts The end of the First Book THE COMPLEAT SURVEYOR The Second Book THE ARGVMENT IN this Book is contained both a generall and particular description of all the most necessary Instruments belonging to Surveying as the Theodolite Circumferentor and Plain Table with all the appurtenances thereunto belonging as the Staffe Sockets Screws Index Label and other necessaries Now whereas these three Instruments are the most convenient for all manner of practises in Surveying I have so ordered the matter that in this Book after the Theodolite and Circumferentor are particularly described as they have usually been made I come to the description of the Plain Table and therein have shewed how that Instrument may be ordered to performe the work of any of the other so that whatsoever may be done by the Theodolite Circumferentor or any other Instrument the same may be effected by the Plain Table onely as it is there contrived with the same ease dispatch and exactnesse and in many respects better as in Chap. 1. doth plainly appear so that this Instrument onely is sufficient for all manner of practises whatsoever And besides the fore-mentioned Instruments for mensuration there is described divers other Instruments belonging thereunto as Chains Scales Protractors and the like all which are described according to the best contrivance yet known A DESCRIPTION OF INSTRVMENTS CHAP. I. Of Instruments in generall THe particular description of the severall Instruments that have from time to time been invented for the practise of Surveying would make a Treatise of it self and in this place is not so necessary to be insisted on every of the inventors in their severall Books of the uses of them having been already large enough in their construction To omit therefore the description of the Topographicall Instrument of Master Leonard Diggs the Familiar Staffe of Master John Blagrave the Geodeticall Staffe and Topographicall Glasse of Master Arthur Hopton with divers other Instruments invented and published by Gemma Frisius Orentius Clavius Stofterus and others I shall immediately begin with the description of those which are the ground and foundation of all the rest and are now the only Instruments in most esteem amongst Surveyors and those are chiefely these three the Theodolite the Circumferentor and the Plain Table Now as I would not confine any man to the use of one particular Instrument for all employments so I would advise any man not to cumber himselfe with multiplicity since these three last named are sufficient for all occasions And if I should confine any man to the use of any one of these Instruments as for a shift any one of them will perform any kinde of work in Surveying yet in that I should do him injury for in many cases one Instrument may make a quicker dispatch and be altogether as exact as another As in laying down of a spacious businesse I would advise him to use the Circumferentor or Theodolite and for Townships and small Inclosure the Plain Table so altering his Instrument according at the nature or quality of the ground he is to measure doth require These three speciall Instruments have been largely described already by divers as namely by Master Diggs Master Hopten Master Rathborne and last of all in Planometria yet in this place it will be very necessary to give a particular description of them again because if any man have a desire to any particular Instrument he may give the better directions for the making thereof For the description which I shall make of these three Instruments in particular it shall be agreeable to those Instruments as they are usually made with some small addition or alteration But when I come to the description of the Plain Table after that I have described it according to the vulgar way I will then shew you a new metamorphosis of that Instrument making it the most absolute and universall Instrument yet ever invented so that having that one Instrument made according to the following directions you shall have need of no other for the due exact and speedy performance of any thing belonging to the Art of Surveying The Plain Table used as the Theodolite For the Frame of the Table being graduated according to that description will be an absolute Theodolite and perform the work thereof with the same facility and exactnesse and whatsoever may be done by the limbe of the Theodolite the same the degrees on the frame of the Table will as well perform The Plain Table used as a Circumferentor Likewise the Index and Sights together with the Box and Needle being taken from the Table and screwed to the Staffe as in the description thereof it is so conveniently ordered will be an absolute Circumferentor and in some respects better then the ordinary one hereafter described because the Sights thereof stand at a greater distance so that thereby the visuall line may be the better directed The plain Table not one but all Instruments And this Instrument as now contrived though it be called the Plain Table only yet you see that it contains both the other and therefore in advising any man to the use thereof chiefely I do not confine him to one but to all Instruments and therefore do not contradict my former expression Besides there is another great convenience which doth ensue by the degrees on the Tables frame for in taking the plot of a field according to the following directions by the Plain Table you may at the same time perform the same work by the degrees on the frame of the Table if at the drawing
a line into such equall parts so that your stationarie distance KL may contain 800 of them Your Scale being thus made take in your Compasses the distance between any two marks or places here described and apply it to your Scale so shall it exactly shew you the true distance between the two places so taken in the same parts as the the line KL was divided In this manner may you with speed and exactnesse attein the true distance and scituation of any Mark or Marks far remote without approaching neer any of them and thus in overgrown land where you can neither go about it nor measure within it this Chapter will be of excellent use CHAP. XVI How to take the true plot of a field at one station taken within the same field so that from thence you may see all the angles of the same field by the Plain Table WHen you enter any field to survey your first work must be to set up some visible mark at each angle thereof or let one go continually before you to every angle holding up a white cloth or the like to direct you which being done make choice of some convenient place about the middle of the field from whence you may behold all your Marks and there place your Table covered with a sheet of paper the needle hanging directly over the Meridian line of the Card which you must alwayes have regard unto especially when you are to survey many fields together Then make a mark about the middle of your paper which shall represent that part of the field where your Table standeth and laying the Index unto this point direct your sights to the severall angles where you before placed your marks and draw lines by the side of the Index upon the paper then measure the distance of every of these marks from your Table and by your Scale set the same distances upon the lines drawn upon the Table making small marks with your Protracting pin or Compasse point at the end of every of them then lines being drawn from one to another of these points you shall have upon your Table the exact plot of your Field all the lines and angles upon the Table being proportional to those of the Field Suppose you were to take the plot of the Field ABCDEF Having placed marks in the severall angles thereof make choise of some convenient place about the middle of the Field as at L from whence you may behold all the marks before placed in the severall angles and there place your Table then turn your Instrument about till the needle hang over the Meridian line of the Card the North end of which line is noted with a Flower-de-luce and is represented in this figure by the line NS Your Table being thus placed with a sheet of paper thereupon make a mark about the middle of your Table which shall represent that place in the field where your Table standeth then applying your Index to this point direct the sights to the first mark at A and the Index resting there draw a line by the side thereof to the point L then with your Chain measure the distance from L the place where your Table standeth to A your first mark which suppose to be 8 Chains 10 Links then take 8 Chains 10 Links from any Scale and set that distance upon your Table from L to A and at A make a mark Then directing the sights to B your second mark draw a line by the side of your Index as before and measure the distance from your Table at L to your mark at B which suppose 8 Chains 75 links this distance must be taken from your Scale and set upon your Table from L to B and at B make another mark Then direct the sights to the third mark C and draw a line by the side of the Index measuring the distance from L to C which suppose 10 Chains 65 links this distance being taken from your Scale and applyed to your Table from L to C shall give you the point C representing your third mark In this manner you must deale with the rest of the marks at D E and F and more if the field had consisted of more angles Lastly when you have made observation of all the marks round the Field and found the points A B C D E and F upon your Table you must draw lines frnm one point to another till you conclude where you first began as draw a line from A to B from B to C from C to D from D to E from E to F and from F to A where you began then will ABCDEF be the exact figure of your Field the sides and angles of the said figure bearing an exact proportion to those in the Field and the line NS in this and the following figures alwayes representeth the Meridian line CHAP. XVII How to take the plot of a field at one station taken in the middle thereof by the Theodolite PLace marks at the severall angles of the Field as before and make choice of some convenient place about the middle thereof as L from whence you may see all the marks and there place your Instrument the Needle hanging directly over the Meridian line in the Card. This done direct your sights to the first mark at A noting what degrees the Index cutteth which let be 36 degrees 45 minutes these 36 degrees 45 minutes must be noted down in your Field-book in the first and second Columns thereof Then measure the distance from L the place of your Instrument to A your first mark which let contain 8 Chains 10 Links these 8 Chains 10 Links must be placed in the third and fourth Column of your Field-book as hath been directed in the description thereof Then direct the sights to B your second mark and note the degrees cut by the Index which let be 99 degrees 15 minutes and the distance LB 8 Chains 75 Links the 99 degrees 15 minutes must be noted in the first and second Columns of your Field-book and the 8 Chains 75 Links in the third and fourth Columns Then direct your sights to C your third mark and note the degrees cut by the Index which let be 163 degrees 15 minutes and let the distance LC be 10 Chains 65 Links the 163 degrees 15 minutes must be noted in the first and second columns of your field-book and the 10 Chains 65 Links in the third and fourth columns thereof Then direct your sights to D your fourth mark and note the degrees cut by the Index which let be 212 degrees ¶ And here you must note that in using the degrees on the frame of the Table that after the Index hath passed 180 degrees which is at the line NS representing alwayes the Meridian line you must then count the degrees backward according as they are numbered on the frame of the Table from 190 to 360. Then measure the distance LD which let be 8 Chains 53 Links the 212 degrees must be noted in
and through it draw the line BC containing 6 Chains 83 Links 3. Place the center of the Protractor on the point C the Meridian line thereof lying parallel to one of the pricked Meridians drawn on the paper then the degrees cut by the Needle at your third observation at C being above 180 namely 216 degrees 30 minutes therefore must the Semicircle lie downwards then making a mark against 216 degrees 30 minutes through it draw the line CD containing 7 Chains 82 Links 4. Lay the center of the Protractor upon the point D the degrees cut by the Needle at that angle being 325 which being above 180 lay the Semicircle of the Protractor downwards and against 325 degrees make a mark with your protracting pin through which point and the angle D draw the line DE making it to contain 6 Chains 96 links 5. Remove your Protractor to E laying the Meridian line thereof upon or parallel to one of the Meridians drawn upon your paper and because the degrees cut by the Needle at this angle were lesse then 180 namely 12 degrees 30 minutes therefore lay the Semicircle of the Protractor upwards and make a mark against 12 degrees 30 minutes through which draw the line EF containing 9 Chains 71 Links 6. Lay the center of the Protractor upon the point F and because the degrees to be protracted are above 180 viz. 342 degrees 30 minutes lay the Semicircle of the Protractor downwards and make a mark against 342 degrees 30 minutes drawing the line FG which contains 7 Chains 54 Links And in this manner must you protract all the other angles G H and K and more if the field had consisted of more angles alwayes observing this for a generall rule to lay the meridian line of the Protractor upon or parallel to one of the Meridians drawn upon your paper which the small divisions at each end of the Scale of the Protractor will help you to do and if the degrees you are to protract be lesse then 180 as those at G H and K are to lay the Semicircle of the Protractor upwards or from you and if they be above 180 degrees as those at A B C and D are to lay the Semicircle downwards as you see done in the figure CHAP. XXXVII How to take the Plot of any Park Forrest Chase Wood ot other large Champion plain by the Index and Needle together with the degrees on the frame of the Table most commodiously supplying the use of the Peractor THe use of the Plain Table Theodolite and Circumferentor hath been sufficiently taught in the preceding Chapters and their agreement in all kinde of practises fully intimated so that you may perceive by what hath been hitherto delivered that for some kinde of works one Instrument is better then another and for large and spacious businesses the Circumferentor is the best the Needle being good and no impediment neere to hinder the playing or vertue thereof there being only this objection to be made against it viz. that the degrees in the Card are for the most part so small that they cannot be truly estimated and so may occasion the greater errour in protraction For the salving of this grand inconvenience Master Rathborn hath a contrivance in his Book of Surveying by an Instrument which he calleth a Peractor which is no other then a Theodolite only the Box and Needle is so fitted to the center of the Instrument that when the Instrument is fixed in any position whatsoever the Index may be turned about and yet the Box and Needle remain immoveable The benefit of this contrivance is that whereas in the Circumferentor the degrees are cut by the Needle here the same degrees are cut by the Index and therefore are larger the use whereof is thus Place the Peractor at any angle of a field and turn it about till the Needle hang directly over the Meridian line in the Card then fix the Instrument there and turn the Index about till through the sights you espie the mark or angle you would looke at then shall the Index cut the same degrees and minutes upon the Limbe of the Peractor as the Needle would have cut upon the Card of the Circumferentor if used as is before taught yet notwithstanding this contrivance you see you must be beholding to the Needle the convenience only being that the degrees which you are to note in your Field-book are larger upon the limb of the Instrument then in the Card which I confesse is somthing considerable Let ABCDE be a Field to be measured by the Index and Needle on the Plain Table supplying the use of the Peractor 1. Place your Instrument at A laying the Index and sights with the Box and Needle screwed thereto upon the Diameter of the Table then the Index so lying turn the whole Instrument about till the Needle hang directly over the Meridian line in the Card then screw the Instrument fast and turn the Index about upon the center till through the sights you espie your second angle at B then you shall see that the South end of the Needle will cut upon the Card in the Box about 218 degrees and the Index at the same time upon the Table will cut 218 degrees 10 minutes which must be noted down in your Field book as hath been severall times before taught and measure the distance AB 9 Chains 65 Links which you must note down in your Field-book also ¶ By this you may see the convenience of counting the degrees cut by the Index rather then by the Needle as here you see 10 minutes are lost in estimation which the Index giveth more precisely nay somtimes you may possibly misse halfe or a whole degree by the Needle 2. Place your Instrument at B laying the Index on the diameter thereof and turn the Instrument about till the Needle hang over the Meridian line in the Card then fixing the Instrument there turn the Index and sights to C so shall both the Needle in the Box and the Index on the frame of the Table cut 298 degrees 30 minutes and measuring the distance BC you shall finde it to contain 9 Chains 28 Links the degrees and minutes and the length of the line measured must be noted down in your Field-book as before 3. Place your Instrument at C and lay the Index and sights upon the diameter thereof then turn the Instrument about till the Needle hang over the Meridian line then fixing it there turn the Index about till through the sights you espie the fourth angle at D then will both the Needle and Index cut 15 degrees 40 minutes these degrees and minutes with the measured distance CD 5 Chains 70 Links must be set down in your Field-book 4. Your Instrument being placed at D with the Index on the diameter thereof turn it about till the Needle hang over the Meridian line and there fixing it turn the Index about till through the sights you see the next angle at E then
and dale as before and to this perpendicular CH set the number as you finde it by the Chain then finde the perpendicular IE and measure that with your Chain also all which lines in respect of the hils and vallies will be found much longer then if they were measured by your Scale then by the measured lines BD CH and IE cast up the content of the Trapezia BCDE In this manner you must cast up the content of the Trapezia ABEG and the Triangle GEF and this is the exactest way I can prescribe for the mensuration of uneven grounds which being well and carefully performed will not vary much of the true content For it is apparent that if such mountanous grounds were plotted truly according to their area in plano the figure thereof would not be contained within its proper limits and being laid down amongst other grounds would swell beyond the bounds and force the adjoyning grounds out of their places now for distinction in your Plot you may shadow them off with hils as in this figure lest any man seeing your plot should measure by your Scale and finde your work to differ CHAP. XLVIII How to take the Plot of a whole Mannor or of divers parsels of Land lying together whether Wood-lands or Champion plains by the Plain Table ALthough practise in the performance hereof be better then many words and that the rules already delivered are of sufficient extent to perform the work of this Chapter yet for farther satisfaction in this particular I will herein deliver the most sure and compendious way I can imagine Suppose therefore that the following figure ALMNPQSTYXGH and K were part of a Mannor or divers parcels of land lying together and that it were required to take the plot thereof upon your Plain Table Now the best way in my opinion is first to go round about the whole quantity to be measured and draw upon your Table a perfect plot thereof as if it were one entire field which you may do by the 31 Chap. of this Book and then to make separation and division thereof in an orderly way as is taught in this Chapter But before you begin your work it will be very necessary to ride or walke about the whole Mannor or at least so much as you are to survey that you may be the better acquainted with the severall bounders and in your passage you ought to take speciall notice of all eminent things lying in your way as Churches Houses Mils High-wayes Rivers c. which will much help you also in this your passage it were necessary to take notice of some convenient place to begin your work as followeth Having made choice of some convenient place in the peripherie or outward part of the Mannor as at A place there your Table turning it about till the Needle hang over the Meridian line in the Card and there fix it then upon the Table with most convenience assigne any point at pleasure as A unto which point lay the Index and turn it about till through the sights you see a mark set up at the next angle at L then by the side of the Index draw the line AL which suppose to contain 8 Chains 68 links take these 8 Chains 68 links from any Scale and place that length upon your Table from A to L. 3. Remove your Table to M and lay the Index upon the line ML turning the Table about till through the sights you espie a mark set up at the angle L where your Table last stood and there fixing it you shall still finde the Needle to hang directly over the Meridian line if you proceed truly in your work then laying the Index to the point M turn it about till through the sights you espie some mark set up at the next angle at N and draw a line by the side of the Index then measuring with your Chain from M to N you shall finde it to contain 7 Chains 27 links which take from the same Scale as before and place the length thereof upon your Table from M unto N. 4. Place your Instrument at N laying the Index upon the line NM and turn the Table about till through the sights you see a mark set up at your former station at M and there fix the Table so will the needle hang over the meridian line as before then turn the Index about upon the point N till through the sights you espie the next angle at P and draw a line by the side thereof then measure the distance NP 9 Chains 32 links which take from the Scale and set it upon your Table from N unto P. In this manner must you go round about the whole Mannor making observation at every angle thereof as at P Q S T Y X G H and K and setting down the length of every line upon your Table as you finde it by measuring with your Chain you shall have upon your Table the figure of one large plain which must include all the rest of the work and in thus going about you shall if you have truly wrought all the way finde your plot to close exactly in the point A where you began but if it do not go over your work again for otherwise all that you do afterwards within the same will be false ¶ Here note that if one sheet of paper will not contain your whole plot you must then shift your paper in this manner when any line falleth off of your Table draw two lines at right angles crosse your paper which the equall divisions on the frame will help you to do then lay another clean sheet of paper upon your Table and by the same parallel divisions at the contrary end of the Table draw two other lines at right angles and upon them note what part of your Plot crossed the two other lines before drawn and at those points begin to go forward with the rest of your work and thus may you shift divers papers one after another if need be Having thus drawn the true plot of the outward bounds or peripherie of the whole Mannor upon your Table as the figure ALMNPQSTYXGH and K and exactly closed your plot at A where you began you may proceed now to lay out the severall Closes therein contained in this manner 1. Place your Table at A laying the Index and sights upon the line AL before drawn and turn it about till through the sights you espie the angle L and there fixing it the needle will hang directly over the Meridian line in the Card then turn the Index about upon the point A till through the sights you espie a mark set up at the angle B and by the side of the Index draw the line AB containing 6 Chains 43 Links 2. Remove the Table to B laying the Index on the line BA and turn the Table about till through the sights you see the angle A then fix it and turn the Index about upon B till you see the next
apprehended at the first sight I will therefore instance in the Circumferentor as being most generall Let the example of the last Chapter serve where the figure ALMNPQSTVXGHK represented part of a Mannor Then having provided your Field-book ready ruled you must at the head of one of the leaves thereof write the Title of the Mannor the County in which it is and who is Lord thereof As The Mannor of Elsmore in the County of S. for the Honourable R. B. Lord thereof Then beginning with your first Close write over the head of your Field-book the Tenants name the name of the Close and the tenour by which he holds the same so for the first Close Henry Grey Casbey Close Pasture Free Under this draw a line quite through your Book then beginning to survey this Close place your Instrument at A and direct your sights to L noting the degrees there cut which let be 160 degrees 45 minutes which 160 degrees 45 minutes must be noted in the first and second Columns of your Field-book then measure the distance AL 8 Chains 68 Links which place in the third fourth Columns 2. Remove your Instrument to L and direct the sights to M the needle cutting 181 degrees 30 min. and the line LM containing 6 Chains 55 Links which note down in your Field-book 3. Place your Instrument at M and direct the sights to N the needle cutting 233 degrees and the line MN 7 Chains 27 Links which note in your Field-book And in regard you are to leave the hedge or bounder ALMN adjoyning to Wisby Common which appertaineth to another Mannor and therefore only the name inserted for your remembrance when you come to protraction you must draw a line quite through your Field Book and in the last Column thereof write Wisby Common which denotes unto you that you are to leave the bounder of Wisby Common 4. Place your Instrument at N and direct the sights to O the needle cutting 355 deg 40 min. and the distance NO being 4 Chains 45 Links which note in your Field-book as before 5. Place your Instrument at O and direct the sights to C the needle cutting 309 degrees 30 minutes and the line OC containing 6 Chains 64 Links which note in your Field-book Now because at these two observations you went against the hedge or bounder of Banton plain you must against them write in your Field-bok Banton plain and because you are now to leave the hedge or bounder of Banton plain draw a line quite through your Field-book 6. Place your Instrument at C and direct the sights to B the needle cutting 54 degrees 00 minutes and the distance CB being 8 Chains 5 Links the degrees and minutes must be noted in the first and second columns of your Field-book and the Chains and Links in the third and fourth 7. Remove your Instrument to B and direct the sights to A the needle cutting 19 degrees 30 minutes and the distance BA being 6 Chains 43 Links the degrees and minutes must be noted in the first and second Columns of your Field-book and the Chains and Links in the third and fourth Now because at these two last observations you went against the hedge or bounder of Bay Wood you must therefore against them write Bay Wood and because you have now finished your first Close you must draw a double line through your Book for your remembrance Then consider which parcell is next fittest to be taken in hand which let be Bay Wood and withall at what angle thereof it is most meet to begin which suppose C and here for your help when you come to protraction you must expresse in the title of this second Close at what angle you begin the same unlesse you had begun it where you ended the last at A and then it is not materiall wherefore seeing you are best to begin at C looke in your Field-book on the work of the last Close what degrees and minutes the needle cut at C which were 54 degrees and 8 Chains 5 Links therefore against that number make this ☉ or the like mark and write the Title for your second Close thus Samuel White Bay-wood by Lease begin at ☉ By this means you shall readily know when you come to protraction where to begin with this prcell and in the margine place 2 for the number of your second parsell and then proceed in your work of surveying this parcell as before you did for the other till you have gone round about the same ending at A where you first began noting down all your observations both of lines and angles with the particular bounders as you go along in your Field-book in all respects as you did those of the first Close and in thus doing you shall finde that at your first observation from C to E that you went partly by the hedge or bounder of Banton plain and partly by the hedge or bounder of Church-field and therefore against the degrees of that observation write Banton plain and Church-field there drawing a line then at your two next observations at E and F you went along the hedge or bounder of Church-field and at the three last observations at G H and K you went against the hedge or bounder of Wisby Common there finishing your second parsell wherefore draw a double line quite through your Field-book These two parcels being finished consider which is next fittest to be taken in hand and where to begin it which suppose Banton plain and to begin at N wherefore looke in your field-book what degrees the needle cut when you made observation at N in the surveying of Gosby Close and left the bounder of Wisby Common which degrees you shall finde to be 355 degrees 40 minutes and 4 Chains 45 Links therefore at the end of that line where you finde 355 degrees 40 minutes and 4 Chains 45 Links make this + or some other mark for a remembrance when you come to protraction then for the next parcell write in your Field-book George Burton Banton plain for two lives begin at ✚ This being done place your Instrument at N and direct the sights to P the needle cutting 220 degrees 20 minutes and the line NP containing 9 Chains 32 Links which note in your Field-book and because at this observation you went by the hedge or bounder of Wisby Common and are now to leave it therefore draw a line and write Wisby Common and in this manner must you go about this parcell also till you come to close at D and having finished draw a double line Then considering that Church field is next fitest to be surveyed and that it is most convenient to begin the same at Q therefore looke what degrees the needle cut at Q in the surveying of Banton plain which were 15 degrees 40 minutes â—nd 10 Chains 75 Links against which in your Fild-book make this ♓ or the like mark for your remembrance and for your next Close â—rite in your Field-book as
on the frame of the Table which supplies the use thereof Thirdly When I mention or make use of the Circumferentor I mean the Index with the Box and Needle screwed to the Staffe ¶ Having thus given you a sufficient description of the severall Instruments and their parts I come now to the use of them shewing how any angle in the field may be measured by any of them And 1. How to observe an angle in the Field by the Plain Table Suppose EK and KG to be two hedges or two sides of a field including the angle EKG and that it were required to draw upon your Table an angle equall thereunto First place your Instrument as neer the angular point K as conveniencie will permit turning it about till the North end of the Needle hang directly over the Flower-de-luce in the Box and then screw the Table fast Then upon your Table with your protracting pin or Compasse point assigne any point at pleasure upon the Table and to that point apply the edge of the Index turning the Index about upon that point till through the sights thereof you espie a mark set up at E or parallel to the line EK and then with your protracting pin or Compasse point or Black-lead draw a line by the side of the Index to the assigned point upon the Table Then the Table remaining immoveable turn the Index about upon the same point and direct the sights to a mark set up at G or parallel thereto that is so far distant from G as your Instrument is placed from K and then by the side of the Index draw another line to the assigned point so shall you have drawn upon your Table two lines which shall represent the two hedges EK and KG and those lines shall include an angle equall to the angle EKG and although you know not the quantity of this angle yet you may by the 1 or 2 Chapters of this Book finde the quantity thereof if there were any need for in working by this Instrument it is sufficient only to give the symetry or proportion of angles and not their quantities as in working by the Theodolite or Circumferentor it is Also in working by the Plain Table there needeth no protraction at all for you shall have upon your Table the true figure of any angle or angles which you observe in the field in their true positions without any farther trouble 2. How to finde the quantity of an angle in the field by the Theodolite Let it be required to finde the quantity of the angle EKG by the Theodolite place your Instrument at K laying the Index on the diameter thereof then turn the whole Instrument about the Index still resting on the Diameter till through the sights you espie the mark at E then screwing the Instrument fast there turn the Index about upon the center till through the sights you espie the mark at G then note what degrees on the frame of the Table are cut by the Index which you will finde to be 114 degrees and that is the quantity of the angle EKG 3. How to finde the quantity of any angle in the field by the Circumferentor If it were required to finde the quantity of the former angle EKG by the Circumferentor First place your Instrument as before at K with the Flower-de-luce in the Card towards you then direct your sights to E and observe what degrees in the Card are cut by the South end of the Needle which let be 296 then turning the Instrument about the staffe the Flower-de-luce alwayes towards you direct the sights to G noting then also what degrees are cut by the South end of the Needle which suppose 182 this done alwayes substract the lesser number of degrees out of the greater as in this Example 182 from 296 and the remainder is 114 degrees which is the true quantity of the angle EKG Again the Instrument standing at K and the sights being directed to E as before suppose that the South end of the Needle had cut 79 degrees and then directing the sights to G the same end of the needle had cut 325 degrees now if from 325 you substract 79 the remainder is 246 but because this remainder 246 is greater then 180 you must therefore substract 246 the remainder from 360 and there will remain 114 the true quantity of the inquired angle and thus you must alwayes do when the remainder exceedeth 180 degrees ¶ This adding and substracting for the finding of angles may seeme tedious to some but here the Reader is desired to take notice that for quick dispatch the Circumferentor is as good an Instrument as the best for in going round a field or in surveying of a whole Mannor you are not to take notice of the quantity of any angle but only to observe what degrees the needle cutteth which in those cases is sufficient as will appear hereafter but in taking of distances by the Circumferentor it is altogether necessary as may appear by the 7 Chap. following and for that reason I have here shewed how to finde an angle by the Circumferentor and also that you might thereby perceive what congruity and harmony there is in all the three Instruments 4. How to set the Index and Labell Horizontall upon the Staffe When you have screwed the Index and sights to the Staffe as a Circumferentor before you put the Labell upon the brasse pin or wier you must hang a line and plummet upon that pin and then put on the Label then move the Index up and down till the thred and plummet hang directly upon a line which is gaged from under the pin all along the Sight and then doth the Instrument stand horizontall or levell which it must alwayes do when you take an altitude therewith 5. How to observe an angle of Altitude The Label which is to be hanged on one of the sights of the Circumferentor as was intimated in the description thereof and the Tangent line on the edge of the Index is only for the finding of angles of Altitude and is therefore only usefull in taking of heights and in surveying of mountanous and uneven grounds The manner how to observe an angle of Altitude by this Label and the Tangent line on the Index is thus Suppose CA to be a Tree Tower or Hill whose height were required Your Instrument being placed at B exactly levell direct the sights thereof towards CA and there fix it hanging the Labell on the farthermost fight upon a pin for that purpose then move the Labell too and fro along the side of the Index till through the sight at the end of the Label and by the Pin on which the Label hangeth you espie the very top of the object to be measured at C then note what degree of the Tangent line is cut by the Labell which suppose 30 and that is the quantity of the angle of Altitude it being equall to the angle CBA Thus by the Rules in this Chapter
followeth Thomas King Church field by Lease begin at ♓ Then placing your Instrument at Q direct the sights to S noting the degrees cut and the length of every line measured with your particular bounders as you did in the other Closes before till you come to inclose at G and when you have done draw a double line quite through your Field-book and write the title of the next Close to be surveyed in this manner John Nichols Odcumb Close Free begin at Then placing your Instrument at T direct the sights to Y and note the degrees cut and the lines measured as in those before till you have gon round the field to G. And thus if there were never so many Inclosures you may without confusion easily distinguish the work of the one from the other and be able remembring the premises to draw a plot thereof at any time remembring alwayes that those numbers in the Margent of your Book ought to be placed severally in your Plot in those Closes they represent The Mannor of Elsmore in the County of S. for the Honourable R. B. Lord thereof 1 Henry Grey Cosbey Close Pasture Free 160 45 8 68 Wisby Common 181 30 6 55 233 00 7 27 355 40 4 45 + Banton plain 309 30 6 64 54 00 8 5 ☉ Bay Wood. 19 30 6 43 2 Samuel White Bay Wood by Lease begin at ☉ 320 00 10 22 Banton plain Church field 15 30 5 50 Church field 337 45 6 68 87 30 6 84 Wisby Common 113 30 6 73 153 30 6 69 3 George Burton Banton plain for 2 Lives begin at + 220 20 9 32 Wisby Common 299 30 10 50 The Forrest 15 40 10 75 ♓ Church field 53 30 5 3 4 Thomas King Church field by Lease begin at ♓ 316 20 13 12 The Forrest 17 15 10 83 Church Lane 56 00 6 15 Odcumb Close 24 10 6 38 5 John Nichols Odcumb Close Free begin at 334 30 7 3 Church Lane 48 30 6 25 101 30 6 18 These Instructions being sufficient for the application and use of the Field book I shall desire all men to make frequent triall and practise thereof and compare the Book with the Plot and protracting the same according to the directions hereafter given you will finde it to be most exact and facile Here by the way I might give directions whereby to take in divers severals at once if the bounders be regular which will much ease you both in surveying and protracting but by small practise this and divers other abreviations will appear of themselves I have here added one leafe of your Field-book as it ought to be ruled which take for an example it being the collections of the work of this Chapter with the severall lines angles and bounders as you observed them in your Survey CHAP. L. How to protract or draw the plot of a whole Mannor or of divers inclosures the observations of the severall angles lines and bounders being noted in your Field-book PRovide a Skin of Velom or Parchment or divers sheets of paper neatly fastned together with Mouth-glew according to the magnitude or greatnesse you intend to have your Plot which paper or parchment let be ruled all over with 〈◊〉 parallel lines representing Meridians as is taught in the 36 Chapter of this Book the distance of which lines one from another must not exceed the breadth of the Scale of your Protractor Now suppose you were to protract the observations of the last Chapter laying your Field-book before you consider which way your plot will extend and accordingly begin your work as at the point A upon which point A place the center of your Protractor turning it about till the correspondent divisions at each end of the Scale of the Protractor lie directly upon one of the parallel meridians and staying the Protractor there look in your Field-book what degrees and minutes the needle cut at your first observation at A which were 160 degrees 45 minutes therefore against 160 degrees 45 minutes of your Protractor make a mark and through that mark and the point A draw the line AL containing 8 Chains 68 Links Then place the center of the Protractor upon the point L in all respects as before and finding your next degrees and length to be 181 degrees 30 minutes and the length 6 Chains 55 Links therefore against 181 degrees 30 minutes of your Protractor make a mark and through it draw the line LM containing 6 Chains 55 Links Then place the center of the Protractor upon the point M and looke in your Field-book what degrees were cut at M protract those degrees as before and draw the line MN containing 7 Chains 27 Links Then place the center of the Protractor upon the point N the degrees cut being 355 degrees 40 minutes and the line NO containing 4 Chains 45 Links and because against these 355 degrees 40 minutes you finde in your Field-book this mark + there placed you must therefore with Black lead or the like make the same mark at the point N upon your paper to signifie that you must there begin to protract some other Close In this manner must you proceed with all the other lines and angles as you finde them noted in your Field-book till you have gone over your first Close and closed your plot at A. Having thus finished your first inclosure you must deale in the same manner with the second third and fourth and so on were there never so many And to know where to begin to protract your second inclosure you must have recourse to your Field-book where you shall finde this mark ☉ at which you must begin your second inclosure which is Bay Wood and the like mark upon your paper at the point C which is your remembrancer to put you in minde that at the point C you must begin to protract your second Inclosure as you did your first Close ¶ In this manner of protracting there is no difference nor cautions to be observed more then those already hinted in Chap. 36 and 38 of this Book viz. that if the degrees to be protracted be under 180 to lay the Semicircle of the Protractor upwards or from you and if they be above 180 to lay the Semicircle downwards CHAP. LI. The figure of any plot being given how to inlarge or diminish the same according to any assigned proportion IT may so fall out that when you have taken the plot of a whole Mannor upon your Plain Table in divers sheets of paper or observed the angles and afterwards protracted them as in the two last Chapters it may so fall out that your plot may be either bigger or lesser then is desired now if at any time it be required to inlarge or diminish any plot according to any proportion this Chapter will accomplish your desire The Instruments for the performance hereof are divers as was intimated in the 9 Chapter of the 2 Book Now for generality and exactnesse the two Indexes there spoken of